Related papers: Universality in diffusion-controlled nucleation an…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
Nucleation in supersaturated vapor is investigated with two series of molecular dynamics simulations in the canonical ensemble. The applied methods are: (a) analysis of critical nuclei at moderate supersaturations by simulating equilibria…
Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes…
We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…
Phase separation is not only ubiquitous in diverse physical systems, but also plays an important organizational role inside biological cells. However, experimental studies of intracellular condensates (drops with condensed concentrations of…
We study a class of growth processes in which clusters evolve via exchange of particles. We show that depending on the rate of exchange there are three possibilities: I) Growth: Clusters grow indefinitely; II) Gelation: All mass is…
The emergence of macroscopic coherence in a many-body quantum system is a ubiquitous phenomenon across different physical systems and scales. This Chapter reviews key concepts characterizing such systems (correlation functions,…
Intermediate energy scale physics plays a very important role in non-equilibrium dynamics of quasi-low dimensional cold atom systems. In this article we obtain the universal scaling relations for the generalized reflection coefficient,…
We consider a rate control problem for an $N$-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state…
Diffusion-limited cluster aggregation (DLCA) is a well established model for the formation of highly porous low-density non-equilibrium structures. One of the main conclusions of the previous studies considering this model is that the…
A phase diagram for a one dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding dynamics of the model: strength of disorder and system size. We monitor the successive events of fiber rupture in…
We investigate the evolution of a population of non-interacting particles which undergo diffusion and multiplication. Diffusion is assumed to be homogeneous, while multiplication proceeds with different rates reflecting the distribution of…
Droplet impacts are common in many applications such as coating, spraying, or printing; understanding how droplets spread after impact is thus of utmost importance. Such impacts may occur with different velocities on a variety of…
Reaction-diffusion systems with mass dissipation are known to possess blow-up solutions in high dimensions when the nonlinearities have super quadratic growth rates. In dimension one, it has been shown recently that one can have global…
Numerically efficient transfer matrix technique for studying statistics of coherent adsorbates on small nanotubes has been developed. In the framework of a realistic microscopic model fitted to the data of ab initio calculations taken from…
The nucleation of a droplet of stable cylinder phase from a metastable lamellar phase is examined within the single-mode approximation to the Brazovskii model for diblock copolymer melts. By employing a variational ansatz for the droplet…
A non-trivial interplay of the UV and IR scaling laws, a generalization of the universality is demonstrated in the framework of the massive sine-Gordon model, as a result of a detailed study of the global behaviour of the renormalization…
A simple method to calculate dispersion of the total number of droplets appeared in the process of nucleation caused by the smooth variation of external conditions has been presented. The analytical result for dispersion is compared with…
For one-dimensional growth processes we consider the distribution of the height above a given point of the substrate and study its scale invariance in the limit of large times. We argue that for self-similar growth from a single seed the…
The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state…